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air mixtures at various initial pressures
Journal of Loss Prevention in the Process Industries 16 (2003) 353–361 www.elsevier.com/locate/jlp
High voltage and break spark ignition of propylene/air mixtures at various initial pressures D. Oancea a,∗, Domnina Razus b, V. Munteanu a, Irina Cojocea b b
a Department of Physical Chemistry, University of Bucharest, 4-12 Regina Elisabeta Boulevard, 030018 Bucharest, Romania “I.G. Murgulescu” Institute of Physical Chemistry, Romanian Academy, 202 Spl. Independentei, sector 6, P.O. Box 12-194, Bucharest, Romania
Received 14 April 2003; received in revised form 1 July 2003; accepted 1 July 2003
Abstract The original break spark test apparatus for intrinsically safe circuits was modified to allow the measurements of minimum ignition currents (MICs) at different initial pressures between 20 and 120 kPa. The MICs of different propylene/air mixtures at ambient temperature and at both atmospheric and sub-atmospheric pressures were measured. The corresponding minimum ignition energies (MIEs) using break sparks were calculated and compared with those derived from MIE/quenching distance correlations using high voltage sparks between flanged electrodes. 2003 Elsevier Ltd. All rights reserved. Keywords: Flammable gas mixtures; Intrinsically safe circuit; Break sparks; Inductive–capacitive sparks; Minimum ignition current; Quenching distance; Minimum ignition energy; Methane; Propylene
1. Introduction The ignition of gaseous flammable mixtures by electric sparks has been studied extensively, particularly for the assessment of the potential hazards associated with accidental gas explosions. Many studies were focused on minimum ignition energy (MIE) measurements. For such studies, high voltage capacitive sparks were generally used as ignition sources since their energy can be delivered in a very short time to a small volume and simulate best the sparks produced by the discharge of static electricity. The MIE is given by the threshold high voltage spark energy, Hhv, and can be calculated from the measured capacitance, C, and voltage, V, necessary to produce the electrical breakdown that ignites the fuel/oxidizer mixture:
a low voltage circuit also represents a frequent event in environments with explosion hazard. To ensure intrinsic safety for such equipment, one necessary parameter is the minimum ignition current (MIC). For resistive circuits carrying large currents, the ignition is essentially thermal, due to heating of the wires during the break, when the current density reaches very high values and produces an electric arc. When the circuit contains a significant inductance, which is typical for many devices and instruments, the break sparks capable to ignite a flammable mixture require much lower currents and the stored energy can become preponderantly inductive. The corresponding MIE is given by the threshold break spark energy stored in the inductor, Hbs, and can be calculated in this case from the measured inductance, L, and current intensity, Imin:
Hhv ⫽ C·V2 / 2
Hbs ⫽ L·I2min / 2
(1)
On the other hand, the break sparks produced by electrical equipments implying the mechanical breaking of
∗
Corresponding author. Tel.: +40-213131120; fax: +40-213159249. E-mail address: [email protected] (D. Oancea).
0950-4230/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0950-4230(03)00072-X
(2)
The ignition process was assumed to be quite similar for electrostatic and break sparks, despite of the significant differences between the electrode spacing during the energy release (Litchfield, Kubala, Schellinger, Perzak, & Burgess, 1980). The high voltage capacitive sparks, as well as high voltage inductive–capacitive
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Nomenclature a, b, c fit parameters C capacitance d distance H ignition energy I current k constant L inductance MIC minimum ignition current MIE minimum ignition energy p pressure P potentiometer r correlation coefficient R resistor V voltage f equivalence ratio Subscripts, superscripts bs corr hv min q 0
referring to break-sparks corrected value referring to high-voltage (capacitive and inductive–capacitive) electric sparks minimum value referring to quenching initial value
sparks, taking place across initially separated electrodes, are however more efficient as ignition sources than the break sparks having the same energy but occurring when the circuit is opened. The differences originate in the fraction of the spark energy transferred to electrodes: negligible for high voltage sparks, where the electrodes are separated by a distance greater than or equal to the quenching distance, and significant for the break sparks, where the electrode separation starts from very small values and then continuously increases. An analysis of the differences between the ignition energies obtained from high voltage sparks occurring at quenching or higher distances and low voltage break sparks occurring at lower distances for the same system offers the possibility to estimate the extent of the energy transferred to electrodes, if other phenomena involved in the ignition are neglected. The aim of this paper is to measure MIEs for different propylene/air mixtures, at atmospheric and various subatmospheric initial pressures, using both high voltage and break sparks, and to compare the results. The MIEs for break sparks are calculated from the measured MICs using a circuit containing inductances close to 100 mH. On the other hand, the MIEs referring to high voltage sparks for the same mixtures are indirectly evaluated from the measured quenching distances at various initial
pressures, using a previously found correlation between MIEs and the corresponding quenching distances (Oancea, Popescu, & Ionescu, 1987; Oancea, Razus, & Ionescu, 1992). To validate the experimental and correlation methods additional measurements of MICs and quenching distances are performed for a stoichiometric methane/air mixture and the results are found to agree well with the reference data. The procedures used to measure the ignition energies, at pressures lower than atmospheric, for both low voltage break sparks and high voltage sparks represent an useful extension of the technique devoted to gas phase ignition, including high altitude phenomena. Propylene–air mixtures can be very often encountered in a series of industrial processes connected with both propylene production and its use to obtain polypropylene, acrylonitrile, propylene oxide, cumene and other valuable chemicals, requiring consequently additional information and justifying the interest for this system. The knowledge of experimental data referring to MIC and MIE is a key step in the assessment of risk for industrial equipments where propylene is obtained, stored or processed.
D. Oancea et al. / Journal of Loss Prevention in the Process Industries 16 (2003) 353–361
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2. Experimental apparatus The MIC was determined in a break spark test apparatus for intrinsically safe circuits as described in an international standard (International Electrotechnical Commission, 1990). The apparatus is essentially the same as that developed by PTB (Physikalisch-Technische Bundesanstalt)—Germany and by the Mining Research Establishment—England (Wooding & Shaw, 1957). The stainless steel test explosion cell has a cylindrical form, with a 9.6 cm internal diameter and a 12.2 cm height and it is vacuum- and pressure-tight. It was tested under static pressure within the range of 0.1–5000 kPa. This facility offers thus the possibility to extend intrinsic safety evaluations for gaseous systems at pressures different from ambient, especially at sub-atmospheric ones. The upper lid is provided with a transparent window made from organic glass to ensure a visual or a photoelectric observation of the ignition process. The break sparks are produced between a rotating electrode made from a tungsten wire and each of the two cadmium blocks with a rectangular profile fixed on the lower lid, as shown in Fig. 1. The tungsten wire having a 0.1 mm diameter contains a spring as a middle segment used to obtain a higher speed of the circuit breaking, the distance between wire holder and cadmium electrode being 40 mm. This wire diameter was found to be a good compromise between an easily consumable thin wire (due to wire burn-off) and a thick one that would have resulted in significant energy losses. Alternatively a tungsten wire with a 0.29 mm diameter was also used to verify the effect of electrode thickness. The scheme of the electric circuit is given in Fig. 2. The circuit is fed with 24 V ac and contains a 96 mH inductor, a current limiting resistor R1, two potentiometers P1 and P2 (for rough and fine current adjustment), and the breaking contacts. The electrode holder is connected through a stainless steel rod to an electric motor equipped with a suitable reduction gearing allowing rotation with up to 16 rpm. Teflon gaskets tighten the rotating rod. A counting device is provided
Fig. 1.
Fig. 2. Scheme of the electric circuit for break spark ignition of flammable gaseous mixtures.
to record the number of spins until explosion, when the driving motor is stopped by the photocell signal. It is worth mentioning that, for higher currents, mixed sparks—inductive and thermal—are obtained. This is characteristic for mixtures close to explosion limits at lower pressures, and it was confirmed by the faster consumption of tungsten electrode. High voltage spark MIEs were calculated from the direct measurements of quenching distances and initial pressures using a previously reported correlation (Munteanu, Oancea, & Razus, 2001; Oancea, Razus, Chirila, & Ionescu, 1997; Oancea, Razus, & Munteanu, 2001). The quenching distances were measured in a cylindrical stainless steel test bomb, with the internal diameter and height equal to 6 cm, using flanged electrodes and high voltage capacitive–inductive sparks produced by the discharge of a condenser through a standard induction coil (Oancea et al., 1992) as shown in Fig. 3.
3. MIE/dq correlations A correlation between the MIE of capacitive sparks and the corresponding quenching distance, dq, was frequently sought and reported in literature, based on both experimental and theoretical grounds (Lewis & von Elbe, 1987; van Tiggelen et al., 1968). Recently, assuming that the high voltage MIE delivered as a capacitive spark, Hhv, equals the expansion work of
Schematic drawing of the explosion vessel for break spark ignition experiments.
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4. Experimental procedures
Fig. 3. Schematic drawing of the explosion vessel for quenching distance measurement using high voltage inductive–capacitive sparks. (1) Stainless steel upper lid; (2) Transparent window; (3) Micrometer; (4) Stainless steel lower lid; (5) Gas evacuation/admission tap; (6) Stainless steel disc; (7) Pressure transducer; (8, 9) Insulated stainless steel electrodes with flanges; (10) Ionization gauge.
gases during the formation of the minimal flame, the following simple relationship was obtained (Oancea et al., 1997, 1987): Hhv ⫽ k·p0·d3q
(3)
where k = 0.445 is a constant resulted from the above correlation using the available published data and p0 is the initial pressure of the mixture. This relationship was verified and reported (Oancea et al., 1987) for a large number of data originating in the most reliable literature sources (Bondar, 1967; King & Calcote, 1955; Lewis & von Elbe, 1987). The basic assumption that allows the evaluation of MIE from such correlation, when capacitive–inductive sparks are used instead of capacitive sparks (having different discharging characteristics), implies the equivalence between MIEs required for these two ignition methods. According to this assumption, Hhv calculated from the measurements of quenching distances using more available capacitive–inductive sparks is equivalent to the corresponding MIE measured with capacitive sparks requiring more expensive and complex techniques. The propylene used, 99.5% purity, was purchased from ARPECHIM Plant—Pitesti; methane, 99.0 vol.% purity, was purchased from SIAD, Italy. The fuel–air mixtures were obtained by partial pressures method, in steel cylinders (V = 10 l), at 4 bar total pressure. The components of the vacuum and of pressure line were also previously described (Oancea et al., 1997, 1992).
The current is adjusted at a desired value with potentiometers P1 and P2, when the explosion vessel is filled with air, at a selected pressure. Since the total inductance of the circuit changes noticeably when the coarse range potentiometer P1 is adjusted, due to its additional inductance, the corrected value, Lcorr, should be measured for each value of the electric current. An easier procedure is to use an inductance–current calibration curve. The explosion vessel is then evacuated to less than 1 kPa and subsequently filled with fuel–air mixture at the same total initial pressure. The mixture is admitted and allowed to become quiescent and then the rotation of the wire holder is turned on. At each value of the current, Imin, a series of measurements are made at progressively decreasing total pressure until the ignition no longer occurs after 1000 trials. The critical pressure for ignition is taken as the average of this value and of value immediately above it, when ignition was observed. The pressure range between these two values was usually 0.6–1.0 kPa. At least two replicate measurements were made for each system and the mean value was reported. A similar procedure was used for quenching distance measurements. A value of the separation distance is set between the flanged tips of electrodes and several ignition tests are performed, at decreasing total initial pressures, until no ignition occurs. The average between the pressure when ignition is observed after 10 trials and the last pressure under it, when no ignition occurs, is taken as the critical ignition pressure corresponding to a certain quenching distance. The average value resulted from several measurements is reported.
5. Experimental results 5.1. Introductory experiments with methane/air The break spark test apparatus was verified using a stoichiometric methane/air mixture ([CH4] = 9.50 vol.%), at various initial pressures ranging from 20 to 110 kPa, using tungsten wires of 0.10 and 0.29 mm diameters. The diagram of measured MIC versus pressure is given in Fig. 4. The limiting safe value allowed for the ignition current (0.30 A) in our experimental setup restricts the ignition range of the fuel/air mixtures to very low initial pressures, where higher currents are necessary. Within the mentioned pressure range, the MICs determined with the thinner wire are lower as compared to those determined with a thicker one. Earlier data from Berz (Berz, 1959), when stainless steel wires of various diameters (0.200–0.025 mm) were used to ignite an 8.3 vol.% methane/air mixture have shown the same trend. The decrease of the electrode diameter reduces thus the MIC
D. Oancea et al. / Journal of Loss Prevention in the Process Industries 16 (2003) 353–361
Fig. 4. Minimum ignition currents for a stoichiometric CH4–air mixture, at various initial pressures and two electrode diameters. (쎲) tungsten wire of 0.10 mm diameter; (䊏) tungsten wire of 0.29 mm diameter.
and consequently the corresponding MIE, bringing it to a value close to that obtained from the high voltage discharge. At ambient pressure the MIC is 97.5 and 112.5 mA for wire diameters of 0.10 and 0.29 mm, respectively. For the same methane/air composition and initial pressure, Litchfield and coworkers (Litchfield et al., 1980) reported an ignition current of 111 mA, using a tungsten wire of 0.2 mm diameter. In the same reference (Litchfield et al., 1980), the most readily ignitable mixture of methane and air contains 8.7 vol.% methane and MIC = 96 mA. At a lower methane concentration (8.3 vol.%), measurements performed with a circuit containing a 95 mH inductance, indicated a successful ignition at 190 mA and non-ignition at 180 mA (Wooding & Shaw, 1957). The measured MICs for different initial pressures can be conveniently expressed by the following empirical relationship: Imin ⫽ a ⫹ b·p⫺c 0
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Hbs are shown in Fig. 5 together with Hhv evaluated with correlation Eq. (3) from the measured quenching distances. Reference data measured for high voltage capacitive sparks are also included for comparison. Although the dispersion of literature data originating in different sources is quite large, a very good agreement between directly measured high voltage spark MIE, usually accepted as a reference value, and indirectly via MIE/dq correlation can be observed for atmospheric pressure. It can be also observed that break spark MIE is systematically higher as electrode diameter increases. One can also observe some differences and even inversions at lower pressures, where the weights of various factors affecting the discharge can change. A comparison of the present results with several data from the literature is given in Table 2. In order to validate the correlation Eq. (3), the measured quenching distances using capacitive–inductive sparks are compared with the quenching distances calculated according to Eq. (3) using the most reliable reported values of MIE, measured using capacitive sparks (Lewis & von Elbe, 1987). The results are shown in Fig. 6. Within the dispersion of experimental data, the measured and calculated values are practically the same for mixtures close to stoichiometric composition, indicating that Eq. (3) can be used as a good approximation for the evaluation of the high voltage ignition energy from measured quenching distances, using capacitive– inductive sparks.
(4)
The fit parameters, obtained for the 9.5 vol.% methane/air mixture, are summarized in Table 1. The corresponding MIEs calculated with Eq. (2) as Table 1 Fit parameters of the correlations between MIC (Imin / mA) and total initial pressure (p0/kPa), for a stoichiometric CH4/air mixture [CH4] (vol.%)
a
b
c
r2
Tungsten wire diameter (mm)
9.50
0 0.367
715 1510
–0.417 –0.564
0.984 0.993
0.10 0.29
Fig. 5. MIEs for a stoichiometric methane/air mixture, at various total initial pressures. (䊐) Hhv calculated from quenching distances; (䊊) Hbs calculated from measured MIC, break sparks produced by a tungsten wire of 0.10 mm diameter; (왖) Hbs calculated from measured MIC, break sparks produced by a tungsten wire of 0.29 mm diameter; (★) directly measured Hhv (Lewis & von Elbe, 1987).
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Table 2 MIE (Hbs and Hhv ) of a stoichiometric CH4/air mixture, at ambient initial pressure and temperature Hmin/mJ
Ignition source
Reference
0.45 0.60 0.34 0.33 0.75 0.63
Break sparks, using a tungsten wire of 0.10 mm diameter Break sparks, using a tungsten wire of 0.29 mm diameter Inductive–capacitive sparks Capacitive sparks, ignition probability set to 0.01 Capacitive sparks Capacitive sparks, ignition probability set to 0.80
Present work Present work Oancea et al. (1992) Lewis and von Elbe (1987) King and Calcote (1955) Moorhouse et al. (1974)
Fig. 6. Measured and calculated quenching distances for CH4/air mixtures versus equivalence ratio, at ambient initial temperature and pressure. (왖) calculated dq; (왕) measured dq.
Fig. 7. MICs of propylene–air mixtures. (쎲) 3.33 vol.%; (䊊) 3.84 vol.%; (䉬) 4.35 vol.%; (䉫) 4.55 vol.%; (왔) 5.25 vol.%.
5.2. Main experiments with propylene/air The measurements of MIC for propylene/air were carried out for mixtures with several compositions, at various total initial pressures. Several results are given in Fig. 7, as plots of MIC versus total initial pressure (at different propylene concentrations) and in Fig. 8, as plots of MIC against propylene concentration (at several initial pressures). For all investigated mixtures, the pressure dependence of MIC follows the same pattern, described by the empirical law (4). The fit parameters for propylene/air, in various conditions, are given in Table 3. Polynomial ratios were fitted on the experimental data giving MIC against propylene concentration at various initial pressures. A broad minimum of the curves, associated to the most readily ignitable mixture, is observed around 5.5% propylene (f = 1.25) for all initial pressures. The measured MIEs and quenching distances were used to calculate the corresponding MIEs Hbs and Hhv, respectively. Typical results are given in Figs. 9 and 10. In Fig. 9, the high voltage and break spark MIEs can be
Fig. 8. MICs versus propylene concentration, at various total initial pressures. (쎲) p0 = 40 kPa; (왔) p0 = 60 kPa; (䊏) p0 = 100 kPa.
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Table 3 Fit parameters of the correlations between minimum ignition current (Imin/mA) and total initial pressure (p0/kPa), for several propylene/air mixtures [C3H6] (vol.%)
a
b × 10⫺3 c
3.84 4.35 4.40 4.55 4.70 5.25 5.82 6.55 4.82
50.1 74.0 62.3 57.8 61.2 40.6 56.7 56.6 57.4
8.15 15.0 212 55.3 13.1 3.60 9.16 5.64 5.18
⫺1.06 ⫺1.38 ⫺2.07 ⫺1.62 ⫺1.35 ⫺0.963 ⫺1.27 ⫺1.12 ⫺1.15
r2
Tungsten wire diameter (mm)
0.998 0.984 0.993 0.991 0.996 0.994 0.999 0.978 0.977
0.10
0.29
Fig. 10. MIEs Hbs of different propylene/air mixtures; (tungsten wire of 0.10 mm diameter). (쎲) p0 = 40 kPa; (왔) p0 = 60 kPa; (䊏) p0 = 100 kPa.
For stoichiometric propylene/air mixture, the MIE by break sparks (determined with a 0.10 mm diameter tungsten wire), is close to the ignition energy transferred from inductive–capacitive electric sparks (Oancea et al., 1992) and from capacitive sparks (Bondar, 1967; Calcote, Gregory, Barnett, & Gilmer, 1952). The literature data allow only a comparison for a rich-propylene/air mixture (5.50 vol.% C3H6, which is the most readily ignitable mixture): MIE = 0.25 mJ by break sparks, 0.18 mJ by inductive–capacitive sparks (Oancea et al., 1992) and 0.17 mJ by capacitive sparks (Bondar, 1967; Calcote et al., 1952). Fig. 9. MIEs for a near-stoichiometric propylene–air mixture, at various total initial pressures. (쎲) 4.53% C3H6–air, Hhv calculated from the measured quenching distances; (䊊) 4.55% C3H6–air, Hbs calculated from the measured MICs, using a tungsten wire of 0.29 mm diameter.
compared to each other and, in Fig. 10, the break spark MIEs are plotted against propylene concentration. It can be observed that high voltage MIEs is more efficient than the break spark MIEs when tungsten wire diameter is 0.29 mm (Fig. 9). When tungsten wire diameter is 0.10 mm the differences between high voltage MIEs and break spark MIEs are within experimental errors, indicating that the ignition process is similar in both cases. The same trend found for pressure (at constant fuel concentration) and concentration (at constant total initial pressure) dependence of MIC, for propylene/air mixtures, is also observed in the plots of Hbs against pressure and concentration, respectively (Figs. 9 and 10). In Table 4, the results are listed together with the available literature data.
6. Conclusions The original break spark test apparatus for intrinsically safe circuits was modified to allow measurements of minimum ignition currents at different initial pressures between 20 and 120 kPa. This extension allows the calculation of the corresponding break spark MIEs, which can be compared with the high voltage MIEs in order to establish the relative efficiency of break spark and high voltage ignition. Minimum ignition currents of different propylene–air mixtures within the explosivity range at ambient temperature and at both atmospheric and sub-atmospheric pressures were measured and the corresponding MIEs were calculated. The quenching distances of the same mixtures were measured using high-voltage inductive– capacitive sparks generated between flanged electrodes and the corresponding MIEs of the high voltage sparks were calculated using a correlation equation. It has been found that the break spark ignition is simi-
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Table 4 MIE (Hbs and Hhv) of two propylene/air mixtures, at ambient initial pressure and temperature Hmin/mJ
Ignition source
Reference
4.50% C3H6–air (stoichiometric mixture) 0.28 Break sparks, using a tungsten wire of 0.10 mm diameter (4.40% C3H6) 0.39 Break sparks, using a tungsten wire of 0.29 mm diameter (4.61% C3H6) 0.29 Inductive–capacitive sparks 0.41 Capacitive sparks 0.28 Capacitive sparks
Present work Present work Oancea et al. (1992) Calcote et al. (1952) Bondar (1967)
5.50% C3H6–air (the most readily ignitable mixture) 0.25 Break sparks, using a tungsten wire of 0.10 mm diameter 0.18 Inductive–capacitive sparks 0.17 Capacitive sparks, ignition probability set to 0.80
Present work Oancea et al. (1992) Bondar (1967)
lar to high voltage ignition, within experimental errors, when using tungsten wire of 0.10 mm diameter, and decreases in efficiency as tungsten wire diameter increases. Disregarding the microscopic details of the discharge, this similarity that has been long ago ascertained (Litchfield et al., 1980) could be attributed, at the macroscopic level, to the fast conversion of the discharge energy into the same form of thermal energy which must be supplied to compensate the energy losses during ignition. The break spark MIE for propylene/air mixtures exhibits a broad minimum around 5.5% propylene concentration (f = 1.25) irrespective of the initial pressure. The same behavior has been previously found for high voltage ignition (Oancea et al., 1992). The corresponding values for the most easily ignited mixture are 0.25 mJ for break sparks (tungsten wire diameter 0.10 mm) and 0.18 mJ for high voltage sparks. As expected, the stoichiometric propylene/air mixture is more reactive (Hhv = 0.28 mJ; Oancea et al., 1992) than the corresponding propane/air mixture (Hhv = 0.39 mJ; Lewis & von Elbe, 1987) and less reactive than ethylene/air mixture (Hhv = 0.096 mJ; Calcote et al., 1952). The dependence of MIE on the initial pressure for both break spark and high voltage ignition is quite similar, and can be expressed as a power law function. Again, as expected, MIE progressively increases as initial pressure decreases. The measuring and calculation procedures were verified using a reference stoichiometric methane–air mixture, for which a good agreement with the literature data was found. It can be also concluded that MIE can be practically measured using not only high voltage capacitive sparks requiring expensive equipments, but also break sparks produced between thin electrodes as well as the correlation between the high voltage sparks and the quenching distances. The advantages and limitations of these procedures will be further examined in our future works.
Acknowledgements The authors acknowledge the financial support of the Romanian Ministry of Education and Research under Research Grant no. 32/2002.
References Berz, I. (1959). On inductive break sparks of high incendive power. Combustion and Flame, 3, 131–132. Bondar, V. (1967). Ignition sources and protection methods against static electricity. Jurnal Vsesoyuznovo Himicheskovo Obsichestva imeni Mendeleeva (Journal of “Mendeleev” Russian Chemical Society), 12, 291–298. Calcote, H., Gregory, C., Barnett, C., & Gilmer, R. (1952). Spark ignition. Effect of molecular structure. Industrial and Engineering Chemistry, 44, 2656–2662. International Electrotechnical Commission (1990). Electrical apparatus for explosive gas atmospheres, part 3: Spark-test apparatus for intrinsically-safe circuits (3rd ed.). IEC Publication 79-3. King, I., & Calcote, H. (1955). Effect of initial temperature on minimum spark-ignition energy. Journal of Chemical Physics, 23, 2444–2445. Lewis, B., & von Elbe, G. (1987). Combustion, flames and explosion of gases (3rd ed.). New York: Academic Press. Litchfield, E. L., Kubala, T. A., Schellinger, T., Perzak, F. J., & Burgess, D. (1980). Practical ignition problems related to intrinsic safety in mine equipment. US Bureau of Mines Report 8464. Moorhouse, J., Williams, A., & Maddison, T. E. (1974). An investigation of the minimum ignition energies of some C1 to C7 hydrocarbons. Combustion and Flame, 23, 203–213. Munteanu, V., Oancea, D., & Razus, D. (2001). An alternative method for minimum ignition energy evaluation of gaseous mixtures. Analele Universitatii Bucuresti-Chimie, 10, 35–47. Oancea, D., Razus, D., Chirila, F., & Ionescu, N. I. (1997). Pressure and temperature dependence of the quenching distance for propylene/air mixtures. Revue Roumaine de Chimie, 42, 571–578. Oancea, D., Popescu, D., & Ionescu, N. I. (1987). On the significance of the minimum ignition energy of an explosive gaseous mixture. Revue Roumaine de Chimie, 32, 1211–1218. Oancea, D., Razus, D., & Ionescu, N. I. (1992). Quenching distances and minimum ignition energies of propylene/air gaseous mixtures. Revue Roumaine de Chimie, 37, 95–100. Oancea, D., Razus, D., & Munteanu, V. (2001). Empirical and theor-
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etical correlations between minimum ignition energy and quenching distance. In J. Mikielewicz, J. Dembczynski, P. Wolanski, & S. Szolkowski (Eds.), Proceedings of the 17th International Symposium on Combustion Processes, Poznan. (p. 195). Poznan University of Technology. van Tiggelen, A., Balaceanu, J. C., Burger, J., de Soete, G., Sajus, L.,
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High voltage and break spark ignition of propylene/air mixtures at various initial pressures D. Oancea a,∗, Domnina Razus b, V. Munteanu a, Irina Cojocea b b
a Department of Physical Chemistry, University of Bucharest, 4-12 Regina Elisabeta Boulevard, 030018 Bucharest, Romania “I.G. Murgulescu” Institute of Physical Chemistry, Romanian Academy, 202 Spl. Independentei, sector 6, P.O. Box 12-194, Bucharest, Romania
Received 14 April 2003; received in revised form 1 July 2003; accepted 1 July 2003
Abstract The original break spark test apparatus for intrinsically safe circuits was modified to allow the measurements of minimum ignition currents (MICs) at different initial pressures between 20 and 120 kPa. The MICs of different propylene/air mixtures at ambient temperature and at both atmospheric and sub-atmospheric pressures were measured. The corresponding minimum ignition energies (MIEs) using break sparks were calculated and compared with those derived from MIE/quenching distance correlations using high voltage sparks between flanged electrodes. 2003 Elsevier Ltd. All rights reserved. Keywords: Flammable gas mixtures; Intrinsically safe circuit; Break sparks; Inductive–capacitive sparks; Minimum ignition current; Quenching distance; Minimum ignition energy; Methane; Propylene
1. Introduction The ignition of gaseous flammable mixtures by electric sparks has been studied extensively, particularly for the assessment of the potential hazards associated with accidental gas explosions. Many studies were focused on minimum ignition energy (MIE) measurements. For such studies, high voltage capacitive sparks were generally used as ignition sources since their energy can be delivered in a very short time to a small volume and simulate best the sparks produced by the discharge of static electricity. The MIE is given by the threshold high voltage spark energy, Hhv, and can be calculated from the measured capacitance, C, and voltage, V, necessary to produce the electrical breakdown that ignites the fuel/oxidizer mixture:
a low voltage circuit also represents a frequent event in environments with explosion hazard. To ensure intrinsic safety for such equipment, one necessary parameter is the minimum ignition current (MIC). For resistive circuits carrying large currents, the ignition is essentially thermal, due to heating of the wires during the break, when the current density reaches very high values and produces an electric arc. When the circuit contains a significant inductance, which is typical for many devices and instruments, the break sparks capable to ignite a flammable mixture require much lower currents and the stored energy can become preponderantly inductive. The corresponding MIE is given by the threshold break spark energy stored in the inductor, Hbs, and can be calculated in this case from the measured inductance, L, and current intensity, Imin:
Hhv ⫽ C·V2 / 2
Hbs ⫽ L·I2min / 2
(1)
On the other hand, the break sparks produced by electrical equipments implying the mechanical breaking of
∗
Corresponding author. Tel.: +40-213131120; fax: +40-213159249. E-mail address: [email protected] (D. Oancea).
0950-4230/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0950-4230(03)00072-X
(2)
The ignition process was assumed to be quite similar for electrostatic and break sparks, despite of the significant differences between the electrode spacing during the energy release (Litchfield, Kubala, Schellinger, Perzak, & Burgess, 1980). The high voltage capacitive sparks, as well as high voltage inductive–capacitive
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Nomenclature a, b, c fit parameters C capacitance d distance H ignition energy I current k constant L inductance MIC minimum ignition current MIE minimum ignition energy p pressure P potentiometer r correlation coefficient R resistor V voltage f equivalence ratio Subscripts, superscripts bs corr hv min q 0
referring to break-sparks corrected value referring to high-voltage (capacitive and inductive–capacitive) electric sparks minimum value referring to quenching initial value
sparks, taking place across initially separated electrodes, are however more efficient as ignition sources than the break sparks having the same energy but occurring when the circuit is opened. The differences originate in the fraction of the spark energy transferred to electrodes: negligible for high voltage sparks, where the electrodes are separated by a distance greater than or equal to the quenching distance, and significant for the break sparks, where the electrode separation starts from very small values and then continuously increases. An analysis of the differences between the ignition energies obtained from high voltage sparks occurring at quenching or higher distances and low voltage break sparks occurring at lower distances for the same system offers the possibility to estimate the extent of the energy transferred to electrodes, if other phenomena involved in the ignition are neglected. The aim of this paper is to measure MIEs for different propylene/air mixtures, at atmospheric and various subatmospheric initial pressures, using both high voltage and break sparks, and to compare the results. The MIEs for break sparks are calculated from the measured MICs using a circuit containing inductances close to 100 mH. On the other hand, the MIEs referring to high voltage sparks for the same mixtures are indirectly evaluated from the measured quenching distances at various initial
pressures, using a previously found correlation between MIEs and the corresponding quenching distances (Oancea, Popescu, & Ionescu, 1987; Oancea, Razus, & Ionescu, 1992). To validate the experimental and correlation methods additional measurements of MICs and quenching distances are performed for a stoichiometric methane/air mixture and the results are found to agree well with the reference data. The procedures used to measure the ignition energies, at pressures lower than atmospheric, for both low voltage break sparks and high voltage sparks represent an useful extension of the technique devoted to gas phase ignition, including high altitude phenomena. Propylene–air mixtures can be very often encountered in a series of industrial processes connected with both propylene production and its use to obtain polypropylene, acrylonitrile, propylene oxide, cumene and other valuable chemicals, requiring consequently additional information and justifying the interest for this system. The knowledge of experimental data referring to MIC and MIE is a key step in the assessment of risk for industrial equipments where propylene is obtained, stored or processed.
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2. Experimental apparatus The MIC was determined in a break spark test apparatus for intrinsically safe circuits as described in an international standard (International Electrotechnical Commission, 1990). The apparatus is essentially the same as that developed by PTB (Physikalisch-Technische Bundesanstalt)—Germany and by the Mining Research Establishment—England (Wooding & Shaw, 1957). The stainless steel test explosion cell has a cylindrical form, with a 9.6 cm internal diameter and a 12.2 cm height and it is vacuum- and pressure-tight. It was tested under static pressure within the range of 0.1–5000 kPa. This facility offers thus the possibility to extend intrinsic safety evaluations for gaseous systems at pressures different from ambient, especially at sub-atmospheric ones. The upper lid is provided with a transparent window made from organic glass to ensure a visual or a photoelectric observation of the ignition process. The break sparks are produced between a rotating electrode made from a tungsten wire and each of the two cadmium blocks with a rectangular profile fixed on the lower lid, as shown in Fig. 1. The tungsten wire having a 0.1 mm diameter contains a spring as a middle segment used to obtain a higher speed of the circuit breaking, the distance between wire holder and cadmium electrode being 40 mm. This wire diameter was found to be a good compromise between an easily consumable thin wire (due to wire burn-off) and a thick one that would have resulted in significant energy losses. Alternatively a tungsten wire with a 0.29 mm diameter was also used to verify the effect of electrode thickness. The scheme of the electric circuit is given in Fig. 2. The circuit is fed with 24 V ac and contains a 96 mH inductor, a current limiting resistor R1, two potentiometers P1 and P2 (for rough and fine current adjustment), and the breaking contacts. The electrode holder is connected through a stainless steel rod to an electric motor equipped with a suitable reduction gearing allowing rotation with up to 16 rpm. Teflon gaskets tighten the rotating rod. A counting device is provided
Fig. 1.
Fig. 2. Scheme of the electric circuit for break spark ignition of flammable gaseous mixtures.
to record the number of spins until explosion, when the driving motor is stopped by the photocell signal. It is worth mentioning that, for higher currents, mixed sparks—inductive and thermal—are obtained. This is characteristic for mixtures close to explosion limits at lower pressures, and it was confirmed by the faster consumption of tungsten electrode. High voltage spark MIEs were calculated from the direct measurements of quenching distances and initial pressures using a previously reported correlation (Munteanu, Oancea, & Razus, 2001; Oancea, Razus, Chirila, & Ionescu, 1997; Oancea, Razus, & Munteanu, 2001). The quenching distances were measured in a cylindrical stainless steel test bomb, with the internal diameter and height equal to 6 cm, using flanged electrodes and high voltage capacitive–inductive sparks produced by the discharge of a condenser through a standard induction coil (Oancea et al., 1992) as shown in Fig. 3.
3. MIE/dq correlations A correlation between the MIE of capacitive sparks and the corresponding quenching distance, dq, was frequently sought and reported in literature, based on both experimental and theoretical grounds (Lewis & von Elbe, 1987; van Tiggelen et al., 1968). Recently, assuming that the high voltage MIE delivered as a capacitive spark, Hhv, equals the expansion work of
Schematic drawing of the explosion vessel for break spark ignition experiments.
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4. Experimental procedures
Fig. 3. Schematic drawing of the explosion vessel for quenching distance measurement using high voltage inductive–capacitive sparks. (1) Stainless steel upper lid; (2) Transparent window; (3) Micrometer; (4) Stainless steel lower lid; (5) Gas evacuation/admission tap; (6) Stainless steel disc; (7) Pressure transducer; (8, 9) Insulated stainless steel electrodes with flanges; (10) Ionization gauge.
gases during the formation of the minimal flame, the following simple relationship was obtained (Oancea et al., 1997, 1987): Hhv ⫽ k·p0·d3q
(3)
where k = 0.445 is a constant resulted from the above correlation using the available published data and p0 is the initial pressure of the mixture. This relationship was verified and reported (Oancea et al., 1987) for a large number of data originating in the most reliable literature sources (Bondar, 1967; King & Calcote, 1955; Lewis & von Elbe, 1987). The basic assumption that allows the evaluation of MIE from such correlation, when capacitive–inductive sparks are used instead of capacitive sparks (having different discharging characteristics), implies the equivalence between MIEs required for these two ignition methods. According to this assumption, Hhv calculated from the measurements of quenching distances using more available capacitive–inductive sparks is equivalent to the corresponding MIE measured with capacitive sparks requiring more expensive and complex techniques. The propylene used, 99.5% purity, was purchased from ARPECHIM Plant—Pitesti; methane, 99.0 vol.% purity, was purchased from SIAD, Italy. The fuel–air mixtures were obtained by partial pressures method, in steel cylinders (V = 10 l), at 4 bar total pressure. The components of the vacuum and of pressure line were also previously described (Oancea et al., 1997, 1992).
The current is adjusted at a desired value with potentiometers P1 and P2, when the explosion vessel is filled with air, at a selected pressure. Since the total inductance of the circuit changes noticeably when the coarse range potentiometer P1 is adjusted, due to its additional inductance, the corrected value, Lcorr, should be measured for each value of the electric current. An easier procedure is to use an inductance–current calibration curve. The explosion vessel is then evacuated to less than 1 kPa and subsequently filled with fuel–air mixture at the same total initial pressure. The mixture is admitted and allowed to become quiescent and then the rotation of the wire holder is turned on. At each value of the current, Imin, a series of measurements are made at progressively decreasing total pressure until the ignition no longer occurs after 1000 trials. The critical pressure for ignition is taken as the average of this value and of value immediately above it, when ignition was observed. The pressure range between these two values was usually 0.6–1.0 kPa. At least two replicate measurements were made for each system and the mean value was reported. A similar procedure was used for quenching distance measurements. A value of the separation distance is set between the flanged tips of electrodes and several ignition tests are performed, at decreasing total initial pressures, until no ignition occurs. The average between the pressure when ignition is observed after 10 trials and the last pressure under it, when no ignition occurs, is taken as the critical ignition pressure corresponding to a certain quenching distance. The average value resulted from several measurements is reported.
5. Experimental results 5.1. Introductory experiments with methane/air The break spark test apparatus was verified using a stoichiometric methane/air mixture ([CH4] = 9.50 vol.%), at various initial pressures ranging from 20 to 110 kPa, using tungsten wires of 0.10 and 0.29 mm diameters. The diagram of measured MIC versus pressure is given in Fig. 4. The limiting safe value allowed for the ignition current (0.30 A) in our experimental setup restricts the ignition range of the fuel/air mixtures to very low initial pressures, where higher currents are necessary. Within the mentioned pressure range, the MICs determined with the thinner wire are lower as compared to those determined with a thicker one. Earlier data from Berz (Berz, 1959), when stainless steel wires of various diameters (0.200–0.025 mm) were used to ignite an 8.3 vol.% methane/air mixture have shown the same trend. The decrease of the electrode diameter reduces thus the MIC
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Fig. 4. Minimum ignition currents for a stoichiometric CH4–air mixture, at various initial pressures and two electrode diameters. (쎲) tungsten wire of 0.10 mm diameter; (䊏) tungsten wire of 0.29 mm diameter.
and consequently the corresponding MIE, bringing it to a value close to that obtained from the high voltage discharge. At ambient pressure the MIC is 97.5 and 112.5 mA for wire diameters of 0.10 and 0.29 mm, respectively. For the same methane/air composition and initial pressure, Litchfield and coworkers (Litchfield et al., 1980) reported an ignition current of 111 mA, using a tungsten wire of 0.2 mm diameter. In the same reference (Litchfield et al., 1980), the most readily ignitable mixture of methane and air contains 8.7 vol.% methane and MIC = 96 mA. At a lower methane concentration (8.3 vol.%), measurements performed with a circuit containing a 95 mH inductance, indicated a successful ignition at 190 mA and non-ignition at 180 mA (Wooding & Shaw, 1957). The measured MICs for different initial pressures can be conveniently expressed by the following empirical relationship: Imin ⫽ a ⫹ b·p⫺c 0
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Hbs are shown in Fig. 5 together with Hhv evaluated with correlation Eq. (3) from the measured quenching distances. Reference data measured for high voltage capacitive sparks are also included for comparison. Although the dispersion of literature data originating in different sources is quite large, a very good agreement between directly measured high voltage spark MIE, usually accepted as a reference value, and indirectly via MIE/dq correlation can be observed for atmospheric pressure. It can be also observed that break spark MIE is systematically higher as electrode diameter increases. One can also observe some differences and even inversions at lower pressures, where the weights of various factors affecting the discharge can change. A comparison of the present results with several data from the literature is given in Table 2. In order to validate the correlation Eq. (3), the measured quenching distances using capacitive–inductive sparks are compared with the quenching distances calculated according to Eq. (3) using the most reliable reported values of MIE, measured using capacitive sparks (Lewis & von Elbe, 1987). The results are shown in Fig. 6. Within the dispersion of experimental data, the measured and calculated values are practically the same for mixtures close to stoichiometric composition, indicating that Eq. (3) can be used as a good approximation for the evaluation of the high voltage ignition energy from measured quenching distances, using capacitive– inductive sparks.
(4)
The fit parameters, obtained for the 9.5 vol.% methane/air mixture, are summarized in Table 1. The corresponding MIEs calculated with Eq. (2) as Table 1 Fit parameters of the correlations between MIC (Imin / mA) and total initial pressure (p0/kPa), for a stoichiometric CH4/air mixture [CH4] (vol.%)
a
b
c
r2
Tungsten wire diameter (mm)
9.50
0 0.367
715 1510
–0.417 –0.564
0.984 0.993
0.10 0.29
Fig. 5. MIEs for a stoichiometric methane/air mixture, at various total initial pressures. (䊐) Hhv calculated from quenching distances; (䊊) Hbs calculated from measured MIC, break sparks produced by a tungsten wire of 0.10 mm diameter; (왖) Hbs calculated from measured MIC, break sparks produced by a tungsten wire of 0.29 mm diameter; (★) directly measured Hhv (Lewis & von Elbe, 1987).
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Table 2 MIE (Hbs and Hhv ) of a stoichiometric CH4/air mixture, at ambient initial pressure and temperature Hmin/mJ
Ignition source
Reference
0.45 0.60 0.34 0.33 0.75 0.63
Break sparks, using a tungsten wire of 0.10 mm diameter Break sparks, using a tungsten wire of 0.29 mm diameter Inductive–capacitive sparks Capacitive sparks, ignition probability set to 0.01 Capacitive sparks Capacitive sparks, ignition probability set to 0.80
Present work Present work Oancea et al. (1992) Lewis and von Elbe (1987) King and Calcote (1955) Moorhouse et al. (1974)
Fig. 6. Measured and calculated quenching distances for CH4/air mixtures versus equivalence ratio, at ambient initial temperature and pressure. (왖) calculated dq; (왕) measured dq.
Fig. 7. MICs of propylene–air mixtures. (쎲) 3.33 vol.%; (䊊) 3.84 vol.%; (䉬) 4.35 vol.%; (䉫) 4.55 vol.%; (왔) 5.25 vol.%.
5.2. Main experiments with propylene/air The measurements of MIC for propylene/air were carried out for mixtures with several compositions, at various total initial pressures. Several results are given in Fig. 7, as plots of MIC versus total initial pressure (at different propylene concentrations) and in Fig. 8, as plots of MIC against propylene concentration (at several initial pressures). For all investigated mixtures, the pressure dependence of MIC follows the same pattern, described by the empirical law (4). The fit parameters for propylene/air, in various conditions, are given in Table 3. Polynomial ratios were fitted on the experimental data giving MIC against propylene concentration at various initial pressures. A broad minimum of the curves, associated to the most readily ignitable mixture, is observed around 5.5% propylene (f = 1.25) for all initial pressures. The measured MIEs and quenching distances were used to calculate the corresponding MIEs Hbs and Hhv, respectively. Typical results are given in Figs. 9 and 10. In Fig. 9, the high voltage and break spark MIEs can be
Fig. 8. MICs versus propylene concentration, at various total initial pressures. (쎲) p0 = 40 kPa; (왔) p0 = 60 kPa; (䊏) p0 = 100 kPa.
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Table 3 Fit parameters of the correlations between minimum ignition current (Imin/mA) and total initial pressure (p0/kPa), for several propylene/air mixtures [C3H6] (vol.%)
a
b × 10⫺3 c
3.84 4.35 4.40 4.55 4.70 5.25 5.82 6.55 4.82
50.1 74.0 62.3 57.8 61.2 40.6 56.7 56.6 57.4
8.15 15.0 212 55.3 13.1 3.60 9.16 5.64 5.18
⫺1.06 ⫺1.38 ⫺2.07 ⫺1.62 ⫺1.35 ⫺0.963 ⫺1.27 ⫺1.12 ⫺1.15
r2
Tungsten wire diameter (mm)
0.998 0.984 0.993 0.991 0.996 0.994 0.999 0.978 0.977
0.10
0.29
Fig. 10. MIEs Hbs of different propylene/air mixtures; (tungsten wire of 0.10 mm diameter). (쎲) p0 = 40 kPa; (왔) p0 = 60 kPa; (䊏) p0 = 100 kPa.
For stoichiometric propylene/air mixture, the MIE by break sparks (determined with a 0.10 mm diameter tungsten wire), is close to the ignition energy transferred from inductive–capacitive electric sparks (Oancea et al., 1992) and from capacitive sparks (Bondar, 1967; Calcote, Gregory, Barnett, & Gilmer, 1952). The literature data allow only a comparison for a rich-propylene/air mixture (5.50 vol.% C3H6, which is the most readily ignitable mixture): MIE = 0.25 mJ by break sparks, 0.18 mJ by inductive–capacitive sparks (Oancea et al., 1992) and 0.17 mJ by capacitive sparks (Bondar, 1967; Calcote et al., 1952). Fig. 9. MIEs for a near-stoichiometric propylene–air mixture, at various total initial pressures. (쎲) 4.53% C3H6–air, Hhv calculated from the measured quenching distances; (䊊) 4.55% C3H6–air, Hbs calculated from the measured MICs, using a tungsten wire of 0.29 mm diameter.
compared to each other and, in Fig. 10, the break spark MIEs are plotted against propylene concentration. It can be observed that high voltage MIEs is more efficient than the break spark MIEs when tungsten wire diameter is 0.29 mm (Fig. 9). When tungsten wire diameter is 0.10 mm the differences between high voltage MIEs and break spark MIEs are within experimental errors, indicating that the ignition process is similar in both cases. The same trend found for pressure (at constant fuel concentration) and concentration (at constant total initial pressure) dependence of MIC, for propylene/air mixtures, is also observed in the plots of Hbs against pressure and concentration, respectively (Figs. 9 and 10). In Table 4, the results are listed together with the available literature data.
6. Conclusions The original break spark test apparatus for intrinsically safe circuits was modified to allow measurements of minimum ignition currents at different initial pressures between 20 and 120 kPa. This extension allows the calculation of the corresponding break spark MIEs, which can be compared with the high voltage MIEs in order to establish the relative efficiency of break spark and high voltage ignition. Minimum ignition currents of different propylene–air mixtures within the explosivity range at ambient temperature and at both atmospheric and sub-atmospheric pressures were measured and the corresponding MIEs were calculated. The quenching distances of the same mixtures were measured using high-voltage inductive– capacitive sparks generated between flanged electrodes and the corresponding MIEs of the high voltage sparks were calculated using a correlation equation. It has been found that the break spark ignition is simi-
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Table 4 MIE (Hbs and Hhv) of two propylene/air mixtures, at ambient initial pressure and temperature Hmin/mJ
Ignition source
Reference
4.50% C3H6–air (stoichiometric mixture) 0.28 Break sparks, using a tungsten wire of 0.10 mm diameter (4.40% C3H6) 0.39 Break sparks, using a tungsten wire of 0.29 mm diameter (4.61% C3H6) 0.29 Inductive–capacitive sparks 0.41 Capacitive sparks 0.28 Capacitive sparks
Present work Present work Oancea et al. (1992) Calcote et al. (1952) Bondar (1967)
5.50% C3H6–air (the most readily ignitable mixture) 0.25 Break sparks, using a tungsten wire of 0.10 mm diameter 0.18 Inductive–capacitive sparks 0.17 Capacitive sparks, ignition probability set to 0.80
Present work Oancea et al. (1992) Bondar (1967)
lar to high voltage ignition, within experimental errors, when using tungsten wire of 0.10 mm diameter, and decreases in efficiency as tungsten wire diameter increases. Disregarding the microscopic details of the discharge, this similarity that has been long ago ascertained (Litchfield et al., 1980) could be attributed, at the macroscopic level, to the fast conversion of the discharge energy into the same form of thermal energy which must be supplied to compensate the energy losses during ignition. The break spark MIE for propylene/air mixtures exhibits a broad minimum around 5.5% propylene concentration (f = 1.25) irrespective of the initial pressure. The same behavior has been previously found for high voltage ignition (Oancea et al., 1992). The corresponding values for the most easily ignited mixture are 0.25 mJ for break sparks (tungsten wire diameter 0.10 mm) and 0.18 mJ for high voltage sparks. As expected, the stoichiometric propylene/air mixture is more reactive (Hhv = 0.28 mJ; Oancea et al., 1992) than the corresponding propane/air mixture (Hhv = 0.39 mJ; Lewis & von Elbe, 1987) and less reactive than ethylene/air mixture (Hhv = 0.096 mJ; Calcote et al., 1952). The dependence of MIE on the initial pressure for both break spark and high voltage ignition is quite similar, and can be expressed as a power law function. Again, as expected, MIE progressively increases as initial pressure decreases. The measuring and calculation procedures were verified using a reference stoichiometric methane–air mixture, for which a good agreement with the literature data was found. It can be also concluded that MIE can be practically measured using not only high voltage capacitive sparks requiring expensive equipments, but also break sparks produced between thin electrodes as well as the correlation between the high voltage sparks and the quenching distances. The advantages and limitations of these procedures will be further examined in our future works.
Acknowledgements The authors acknowledge the financial support of the Romanian Ministry of Education and Research under Research Grant no. 32/2002.
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